Least Common Multiple (LCM) of 105 and 155
The least common multiple (LCM) of 105 and 155 is 3255.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 105 and 155?
First, calculate the GCD of 105 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 155 = 0 remainder 105 |
| 2 | 155 ÷ 105 = 1 remainder 50 |
| 3 | 105 ÷ 50 = 2 remainder 5 |
| 4 | 50 ÷ 5 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 22 | 66 |
| 85 and 61 | 5185 |
| 73 and 27 | 1971 |
| 194 and 34 | 3298 |
| 159 and 53 | 159 |